Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to interpolation between data points in their training corpora. In this paper, we consider the challenge of learning representations that support extrapolation. We introduce a novel visual analogy benchmark that allows the graded evaluation of extrapolation as a function of distance from the convex domain defined by the training data. We also introduce a simple technique, context normalization, that encourages representations that emphasize the relations between objects. We find that this technique enables a significant improvement in the ability to extrapolate, considerably outperforming a number of competitive techniques.
Taylor, Jenny A.; Bratton, Benjamin P.; Sichel, Sophie R.; Blair, Kris M.; Jacobs, Holly M.; DeMeester, Kristen E.; Kuru, Erkin; Gray, Joe; Biboy, Jacob; VanNieuwenhze, Michael S.; Vollmer, Waldemar; Grimes, Catherine L.; Shaevitz, Joshua W.; Salama, Nina R.
Abstract:
Helical cell shape is necessary for efficient stomach colonization by Helicobacter pylori, but the molecular mechanisms for generating helical shape remain unclear. We show that the helical centerline pitch and radius of wild-type H. pylori cells dictate surface curvatures of considerably higher positive and negative Gaussian curvatures than those present in straight- or curved-rod bacteria. Quantitative 3D microscopy analysis of short pulses with either N-acetylmuramic acid or D-alanine metabolic probes showed that cell wall growth is enhanced at both sidewall curvature extremes. Immunofluorescence revealed MreB is most abundant at negative Gaussian curvature, while the bactofilin CcmA is most abundant at positive Gaussian curvature. Strains expressing CcmA variants with altered polymerization properties lose helical shape and associated positive Gaussian curvatures. We thus propose a model where CcmA and MreB promote PG synthesis at positive and negative Gaussian curvatures, respectively, and that this patterning is one mechanism necessary for maintaining helical shape.
